Different stabilities for integro-differential evolution equations with nonlocal conditions and application to epidemiology

Integro-differential evolution equations are becoming increasingly popular in many fields because of their ability to model and assess complicated procedures. In this paper, we study different kinds of stabilities for integro-differential evolution equations with nonlocal conditions. The concept of ?-semi-Ulam-Hyers stability, which lies somewhere between the Ulam-Hyers and Ulam-Hyers-Rassias stabilities, will be specifically discussed. To ensure Ulam-Hyers-Rassias stability, ?-semi-Ulam-Hyers stability, and Ulam-Hyers stability for integro-differential evolution equations with nonlocal conditions, this is considered within the framework of suitable metric spaces. We will examine the many situations in which the integrals are specified on both bounded and unbounded intervals. Techniques such as fixed-point arguments and generalizations of the Bielecki metric are utilized. To illustrate the main results, we also provide examples. The epidemiology application for modeling the transmission of infectious diseases served as a source of interest.